Average Error: 0.5 → 0.6
Time: 51.4s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\log \left(\cos^{-1} \left(\log \left(e^{\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}}\right)\right)\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
e^{\log \left(\cos^{-1} \left(\log \left(e^{\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}}\right)\right)\right)}
double f(double v) {
        double r43319025 = 1.0;
        double r43319026 = 5.0;
        double r43319027 = v;
        double r43319028 = r43319027 * r43319027;
        double r43319029 = r43319026 * r43319028;
        double r43319030 = r43319025 - r43319029;
        double r43319031 = r43319028 - r43319025;
        double r43319032 = r43319030 / r43319031;
        double r43319033 = acos(r43319032);
        return r43319033;
}
↓
double f(double v) {
        double r43319034 = 1.0;
        double r43319035 = v;
        double r43319036 = r43319035 * r43319035;
        double r43319037 = 5.0;
        double r43319038 = r43319036 * r43319037;
        double r43319039 = r43319034 - r43319038;
        double r43319040 = r43319036 - r43319034;
        double r43319041 = r43319039 / r43319040;
        double r43319042 = exp(r43319041);
        double r43319043 = log(r43319042);
        double r43319044 = acos(r43319043);
        double r43319045 = log(r43319044);
        double r43319046 = exp(r43319045);
        return r43319046;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.6

    \[\leadsto \cos^{-1} \color{blue}{\left(\log \left(e^{\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}}\right)\right)}\]
  4. Using strategy rm

  5. Applied add-exp-log0.6

    \[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\log \left(e^{\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}}\right)\right)\right)}}\]

  6. Final simplification0.6

    \[\leadsto e^{\log \left(\cos^{-1} \left(\log \left(e^{\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}}\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019119 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))